If they are completing the required courses after the cert expires, they would become certified again. Their new cert expiry date would depend on what you have set for the recertification date.
If they are completing before the window opens, then I'm not aware of another way to get them certified other than getting them to do the course again or as you say manually updating the record.
There's a request in Canny about a feature to allow recertification to be triggered early, feel free to upvote that and add a reply outlining how it would help in your situation.